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Statistical model simulates cicada surges

Statistical model simulates cicada surges

31 January 2024

By comparing periodical cicadas to ferromagnetic spins, researchers explore whether the insects might communicate to synchronize their emergences.

A red-eyed cicada on a plant.
A cicada from a 17-year brood navigates a plant. Credit: Ken Hammond/USDA, CC BY 2.0

For those in the Midwest and Southeast US, get ready: The cicadas are returning. This spring billions of red-eyed insects that have been munching on plant roots for more than a dozen years will emerge from the soil so that they can make noise, mate, and then die. This year is notable because two neighboring broods of periodical cicada—one that appears every 13 years and another every 17—are set to surface. Some (un)lucky Illinois residents may experience the sights and sounds of both broods simultaneously.

Although biologists have spent decades studying periodical cicadas, mysteries remain. Among them is how, once the year of a brood’s emergence arrives, enormous numbers of cicada nymphs tunnel to the surface within just several weeks. Previous research has established that a primary trigger is the soil temperature reaching 18 °C. Yet something as simple as an overlying shade tree can influence local temperatures, and it’s unlikely that nymphs are perfect evaluators of temperature. Raymond Goldstein, Robert Jack, and Adriana Pesci of the University of Cambridge wondered whether the insects communicate to coordinate their emergence.

To test their idea, the researchers turned to an Ising model of ferromagnets, in which the values of atomic spins are influenced by the values of adjacent spins. The applications of the model have extended beyond condensed matter to such subjects as human decision making and reptile skin patterns. The researchers simulated conditions in the underground cicada nymph feeding areas by using archival surface temperature data from Columbus, Ohio, near the site of a comprehensive 1968 study of a 17-year cicada brood. They accounted for microclimates by adding a temperature component that is random but spatially correlated, since a sunny hilltop would not be located next to a shaded valley.

Holes in the ground, surrounded by sticks and leaf litter.
Holes in the ground mark the exit points of 17-year cicadas in Woodbridge, Virginia, in 2013. Credit: Ken Hammond/USDA, CC BY 2.0

Finally, to encode the ability of the nymphs to communicate with their neighbors, the researchers introduced a variable akin to atomic spins. The cicadas would emerge when the value flipped from –1 to +1, a switch that would be triggered primarily by temperature but also by the behavior of nearby nymphs. After running thousands of simulations, the researchers found that the emergence patterns matched closely with those reported in the 1968 study, with a few vast groups surfacing, followed by a lull and then by more cicada surges. That cycle continued for several weeks.

An Ising model can say only so much about cicadas. Although the results square with the 1960s Ohio data, they may not match so nicely with periodical cicadas in other years and at other locations. And, crucially, the research doesn’t provide insight into how nymphs might exchange information underground; Goldstein, Jack, and Pesci leave that work to the ecologists. Whatever the communication method, it would have to be far subtler than the ear-splitting one that millions of Americans will hear this spring. (R. E. Goldstein, R. L. Jack, A. I. Pesci, Phys. Rev. E 109, L022401, 2024.)

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